AffineSubspace.wOppSide_of_left_mem
∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : CommRing R] [inst_1 : PartialOrder R]
[inst_2 : IsStrictOrderedRing R] [inst_3 : AddCommGroup V] [inst_4 : Module R V] [inst_5 : AddTorsor V P]
{s : AffineSubspace R P} {x : P} (y : P), x ∈ s → s.WOppSide x y- Defined in
- Mathlib.Analysis.Convex.Side
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement and proof · cited by 871
- VSub.vsubproof · cited by 817
- SameRayproof · cited by 149
- vsub_selfproof · cited by 74
- AffineSubspace.WOppSidestatement · cited by 50
- SameRay.zero_leftproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- AffineSubspace.wOppSide_iff_exists_leftproof · cited by 5
- AffineSubspace.wOppSide_of_right_memproof · cited by 2
- AffineSubspace.wSameSide_and_wOppSide_iffproof · cited by 2
- Affine.Simplex.wOppSide_affineSpan_faceOpposite_iffproof · cited by 1